Chaos and its Control in a Neuron Network with Time-Varying Delays

Time delays phenomena are frequently found in both biological and artificial neural networks. There are complex dynamic behaviors in time-delayed neuron systems, and even a simplest neural network system consisted with one neuron with time delays could exhibit complex dynamic behaviors. More than one positive Lyapunov exponent may be found in time-delayed chaotic system since the dimension of such system is infinite. So we expect that more secured communication system can be designed. In this paper, a neural network consisted of one neuron with variable time delays is studied. Stability and period solution of the system are analyzed firstly. Chaos phenomenon of the system is illustrated by giving the diagram of bifurcation and the largest Lyapunov exponent. Then a control system based on washout filter for an artificial neural network with variable time delays is considered. With various control parameters, the control system may appear stable, bifurcation and chaos. In addition, stability and the existence of period solution in the control system are investigated; the threshold ranges are discussed and the experiment results are illustrated. The synchronization of chaos in time-delayed neuron system is studied as well. We also design the coupled system and employ Krasovskii-Lyapunov theory to search the synchronization conditions.